Networks and link data

David E. Wojick dwojick at HUGHES.NET
Mon Mar 12 14:39:32 EDT 2007

Sylvan, I think you are right about attention being constrained rather than strictly conserved. Conserved is metaphorical. The basic point is that if I work on one thing I am not working on others.

We are making headway on the etherial aspect of ideas. The semantic web folks are a leading community here. Google's success shows that the words we use are a good indicator of the ideas we express (and presumeably use). What people call (mistakenly I think) semantic structure is in fact part of the structure of our ideas. 

For example, you introduced me to percolation theory. Searching the journals on the referring expression "percolation theory" would give a pretty good picture of where percolation theory was being used, and how it's use has spread over time. Looking at the language that co-occurs with it should show how it is being used as well. So word use is our basic data. In our diffusion work to date we have simply looked at the growth of the use of certain words, using a contagion model to probe the underlying mechanisms.

Beyond words we have structure. An example of structure is our (OSTI's) thing we call Word Web.

It is a complex network in which the nodes are about 30,000 scientific and technical words. There are 3 interlaced subnetworks of pairwise word-word relations. These are "use A for B" or prefered synonyms (about 10,000 pairs); "A is broader than, or narrower than, or a subset of B" (taxonomic, with about 45,000 multi-pair paths), and "A is related to B in some unstated way" (about 200,000 pairs). 

Arguably this network maps the cognitive structure of a broad area of scientific and technical thought in some basic way. It has changed relatively little since it was started in 1973. Here too one could see where a concept like percolation theory was being used and how that was changing over time. In fact we have started doing Pajek mapping of Word Web. In this case we are looking at the diffusion of an idea in a network of ideas, not a network of people.

I myself have been working on the network structure of reasoning, which is arguably what science is all about. My work is about how sentences or whole thoughts, as opposed to words, form networks. I will post on this separately.


>The flow of ideas a very interesting concept. However, measurement is, as you pointed out rather difficult since an idea is a somewhat ethereal concept.
>> This leads to a broader concept which is conserved, which I call
>> "attention." Rather than looking at the movement of an idea from person
>> to person, look at the movement of attention from idea to idea. If we
>> assume that one can only think about one topic at a time then attention
>> is conserved. Thinking about percolation thoery precludes thinking about
>I am not sure about the notion of conservation of attention. The only known conserved entities are physical things like energy, spin, charge, etc. While attention maybe limited or constrained it is unlikely that is conserved at least in the same manner as the conservation of energy. For example each of us has more or less attention at any point in time depending on a variety of factors including such things as health, social and environmental factors, psychological state, etc. While attention maybe a constrained resource it is not clear that is a conserved resource.
>Is it possible that the movement of ideas from person to person is synonymous with the movement of personal attention from idea to idea?
>>As with any applied math, the question is how to apply it to the thing or 
>process under study.
>>For the diffusion of scientific ideas this is a hard problem, because the 
>science of ideas is
>>poorly developed. But I think we are making headway. Thanks for your 
>This is a problem. Until there are ways to measure ideas and their diffusion it might be that these models will have limited value. For sure it will be difficult to calibrate any model to real world situations without the availability of robust indicators derived from real world measures. Of course, complicating matters even more is the possibility that an idea is rarely pure but enmeshed in a complex of other ideas which are implied during the transfer. If the recipient(s) is unaware of the complex then the transfer could be incomplete and have less valuable no matter how much attention the recipient(s) has at his disposal. Very interesting stuff :)
>Dr. J. Sylvan Katz, Visiting Fellow
>SPRU, University of Sussex
>Adjunct Professor
>Mathematics & Statistics, University of Saskatchewan
>Associate Researcher
>Institut national de la recherche scientifique, University of Quebec

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